Photographer 1 charges a $100 fee for a photo shoot plus a rate of $75 per hour. The prices charged by Photographer 2 are shown in the table below.



Photographer 2
Time (hours) Cost (dollars)
0 0
1 125
2 250
3 375

For a 5-hour photo shoot, which photographer would be less expensive? How much less expensive? Show your work.

1 answer

To determine which photographer is less expensive for a 5-hour photo shoot, we can calculate the total cost for each photographer.

Photographer 1

Photographer 1 charges:

  • A base fee of $100
  • An hourly rate of $75 per hour

For a 5-hour photo shoot, the total cost can be calculated as follows:

\[ \text{Total Cost} = \text{Base Fee} + (\text{Hourly Rate} \times \text{Number of Hours}) \] \[ \text{Total Cost} = 100 + (75 \times 5) \] \[ \text{Total Cost} = 100 + 375 \] \[ \text{Total Cost} = 475 \]

Thus, the total cost for Photographer 1 for a 5-hour shoot is $475.

Photographer 2

Photographer 2's prices are given in the table, and we can see the costs for each hour:

  • For 1 hour: $125
  • For 2 hours: $250
  • For 3 hours: $375
  • For 4 hours: The pattern indicates an increase of $125 per hour, so for 4 hours, it would be: \[ 4 \times 125 = 500 \]
  • For 5 hours: Continuing the pattern, we can find that: \[ 5 \times 125 = 625 \]

Thus, for a 5-hour photo shoot, the total cost for Photographer 2 is $625.

Conclusion

Now we can compare the two costs:

  • Cost of Photographer 1 for 5 hours: $475
  • Cost of Photographer 2 for 5 hours: $625

To find out how much less expensive Photographer 1 is than Photographer 2:

\[ \text{Difference} = 625 - 475 = 150 \]

So, Photographer 1 is $150 less expensive than Photographer 2 for a 5-hour photo shoot.

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